Final answer:
To find the difference between changing scale factors, compare the ratios that represent each scale, then subtract one scale factor from the other to get the difference. For instance, the difference between scale factors 1/36 and 1/72 is 1/72, indicating the model with a scale factor of 1/36 is twice as large as the one with 1/72.
Step-by-step explanation:
When looking to find the difference between changing scale factors, you'll need to compare the ratios or proportions that represent each scale. To identify the scale factor, you compare the model or drawing dimension to the actual dimension of the object depicted. For example, a scale of 2:1 implies a scale factor of 1/2, meaning the model or drawing is half the size of the actual object. If comparing two scale factors, subtract one from the other.
For instance, consider two different scale factors, say 1/36 and 1/72, for a model boat with an actual length of 24 feet. To find the difference in scale factors, you calculate 1/36 - 1/72. Converting both fractions to have a common denominator (in this case, 72), we get 2/72 - 1/72, which equals 1/72. The difference between the two scale factors is 1/72, which means that the model using the scale factor of 1/36 will be twice as large as the model with a scale factor of 1/72.